1. Let R be a ring, and let n E N be a natural number. Consider the polynomial ring R[1, . . . , an] in n variables x1, . .., In over R . Show that for any permutation T E Sn = Perm( {1, ..., n} ) of the set {1, ..., n} , there is a unique ring automorphism f, of R[x1, ...,In] which fixes all elements of R and which sends x; to Xx(3) for each i = 1, ..., n